Leafing through Irregular Shapes
By the time middle school students start a prealgebra course, they should have explored a variety of familiar two-dimensional and three-dimensional shapes and should have been exposed to the concepts of perimeter, area, and volume. They know that they can assign numerical values to some attributes of a shape, such as length and surface area. However, my classroom experience confirms the statement that although “students may have developed an initial understanding of area…, many will need additional experiences in measuring directly to deepen their understanding of the area of two-dimensional shapes” (NCTM 2000, p. 242). In addition, the students' previous practice with area is usually with polygons, circles, or a combination of both. However, many real-life objects cannot be described or approximated with simple geometric shapes or with combinations of shapes. Therefore, this activity, which asks students to estimate the area of irregular shapes using finer and finer grids, is not only novel but also a way to apply mathematics to real life.